---
title: "Item Discrimination in Math Garden"
author: "Sharon Klinkenberg"
output: 
  flexdashboard::flex_dashboard:
    logo: http://shklinkenberg.github.io//statistics-lectures/template/logo_uva.png
    orientation: col
    social: menu
    source_code: embed
    vertical_layout: fill
    navbar:
      - { icon: "ion-android-contact", title: "Contact", href: "http://www.uva.nl/en/profile/k/l/s.klinkenberg/s.klinkenberg.html", align: right }
      - { icon: "fa-download", title: "Poster", href: "poster.pdf", align: right }
---

```{r setup, include=FALSE}
library(flexdashboard)
```

Inputs {.sidebar}
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Research

The aim of this study is to find a feasable method to determine item discrimination values within the Math Garden to detect deviant items.

__What is the problem__

* Sparse data
* Scaling
* Identifiability

__Pragmatic solution__

So there are some fundamental problems in estimating a. But can we at least have some pragmatic solution?

__For fancy visuals see QR code__






https://goo.gl/a6ch6A


Column {data-width=500}
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### Discrimination
    
![](Proportion_correct.gif)

   
### Item ratings
    
![](item_distributions.gif)
   
### User Ratings

![](user_distributions.gif)

Column
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### Method

__Simulations__

Simulate responses and response times based on known $\theta$'s, $\beta$'s and $a$-parameters. Look how wel we can recover the $a$-parameter.



* Simulate full data
    * Estimate with LTM
    * GLM
    * Newton-Rapson
    
* Simulate sparse data
    * LTM
    * GLM
    * Newton-Rapson

Look at BIAS and SEM. 

### Proliminary Results

![](scatterplots_for_all_estimation_methods.jpg)

### TO-DO {data-height=200}



* $a = 1$
* $a \sim U(0,3)$
* $a \sim U(-.5,3)$
* Apply NR in Math Garden
* Inactivate bad items
* Apply to real data